Can taking an antibiotic (Augmentin) for sinusitis falsify the test results for syphilis and chlamydia?

No. Augmentin (amoxicillin with clavulanic acid) is a broad-spectrum antibiotic used to treat a wide variety of bacterial infections. Augmentin, as an antibiotic, does not directly affect the results of these serological tests. These tests measure the presence of antibodies against Treponema pallidum, not the direct presence of the bacteria, so the use of antibiotics should not falsify syphilis test results. As with syphilis, Augmentin should not affect the results of diagnostic tests for chlamydia. These tests detect the DNA of the bacterium or its antigens, and the presence of antibiotics should not interfere with the detection technique.

The availability of Augmentin in pharmacies in Poland can be found here:

https://www.gdziepolek.pl/produkty/8049/augmentin-875-mg-125-mg-tabletki-powlekane/apteki

I encourage you to read:

https://www.gdziepolek.pl/kategorie/leki-na-kile-syfilis